The ab initio variational R-matrix method is combined with generalized quantum-defect theory to calculate quantum defect matrices for ${}^1{\Sigma }_u^{+}$ and ${}^1{\Pi }_u$ symmetries of molecular hydrogen. The calculations take account of doubly excited channels and are optimized so as to minimize the dependence of the quantum-defect matrix elements as functions of energy and internuclear distance. The matrices are used to calculate the lowest clamped-nuclei Rydberg potential energy curves as well as doubly excited resonance positions and widths near the first excited state of ${\mathrm{H}}_2^{+}.$ The results are in good agreement with previous ab initio results. Owing to their smoothness, the quantum-defect matrices are well suited for rovibronic multichannel quantum-defect applications. This opens up the possibility of a fully ab initio quantitative theoretical description of excited ${\mathrm{H}}_2,$ including ionization and dissociation.

Fundamental limits on the controllability of quantum mechanical systems are discussed in the light of quantum information theory. It is shown that the amount of entropy-reduction that can be extracted from a quantum system by feedback controller is upper bounded by a sum of the decrease of entropy achievable in open-loop control and the mutual information between the quantum system and the controller. This upper bound sets a fundamental limit on the performance of any quantum controllers whose designs are based on the possibilities to attain low entropy states. An application of this approach pertaining to quantum error correction is also discussed.

We show that the propagation of light in a Doppler-broadened medium can be slowed down considerably even though such medium exhibits very flat dispersion. The slowing down is achieved by the application of a saturating counter propagating beam that produces a hole in the inhomogeneous line shape. In atomic vapors, we calculate group indices of the order of ${10}^3.$ The calculations include all coherence effects.

Quantum theory predicts that two indistinguishable photons incident on a beam-splitter interferometer exit together (the pair emerges randomly from one port or the other). We use a special photon-number-resolving energy detector for a direct observation of this quantum-interference phenomenon. Simultaneous measurements from two such detectors, one at each beam-splitter-interferometer output port, confirm the absence of cross coincidences. Photon-number-resolving detectors are expected to find use in other quantum-optics and quantum-information-processing experiments.

The recent experiments of Zweiback et al. on deuterium clusters irradiated with intense laser beams yielded D-D fusion. This has motivated us to carry out quantum-chemical calculations on a number of deuterium clusters, both neutral and cationic. For doubly charged clusters, in particular ${\mathrm{D}}_{31}^{2+},$ and plainly for more highly charged assemblies, Coulomb explosion of the cluster is in evidence. The quantum-chemical results we present strongly suggest that fragmentation occurs with small groups of deuterium atoms breaking away from the main cluster, such as to leave both small and large fragments with a net charge not exceeding $+|e|.$

We analyze three different quantum search algorithms, namely, the traditional circuit-based Grover’s algorithm, its continuous-time analog by Hamiltonian evolution, and the quantum search by local adiabatic evolution. We show that these algorithms are closely related in the sense that they all perform a rotation, at a constant angular velocity, from a uniform superposition of all states to the solution state. This makes it possible to implement the two Hamiltonian-evolution algorithms on a conventional quantum circuit, while keeping the quadratic speedup of Grover’s original algorithm. It also clarifies the link between the adiabatic search algorithm and Grover’s algorithm.

The study of quantum computation has been motivated by the hope of finding efficient quantum algorithms for solving classically hard problems. In this context, quantum algorithms by local adiabatic evolution have been shown to solve an unstructured search problem with a quadratic speedup over a classical search, just as Grover’s algorithm. In this paper, we study how the structure of the search problem may be exploited to further improve the efficiency of these quantum adiabatic algorithms. We show that by nesting a partial search over a reduced set of variables into a global search, it is possible to devise quantum adiabatic algorithms with a complexity that, although still exponential, grows with a reduced order in the problem size.

The recently developed two-channel Siegert pseudostate method of Sitnikov and Tolstikhin [Phys. Rev. A 67, 032714 (2003)] is here applied to the case of ${\mathrm{Ps}}^{-}$ ${(e}^{+}ee)$ exploiting the hyperspherical elliptic coordinates method. S-wave resonances and antiresonances are calculated and classified according to their locations in the complex plane of the uniformization parameter. The resonance positions and widths are compared to other accurate calculations.

We report calculations for the low-energy near-threshold inelastic collision cross sections between the $\mathrm{Li}\mathrm{}(2s,2p,3s,3p)+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ states. Results are obtained by solving the coupled-channel equations. Order-of-magnitude estimates for higher states have been made with the multichannel Landau-Zener model. Potentials and couplings from H. Croft et al [J. Phys. B 32, 81 (1999)] are employed. The calculated cross sections are much smaller than ones predicted by the classical Thomsom atom formula currently employed in astrophysics. This result is important for the interpretation of stellar spectra.

Correlation images of the symmetric six-electron Coulomb-explosion channel of ${\mathrm{CO}}_2$ were used to isolate specific geometries (linear and bent) for angular-resolved analysis of the Coulomb-explosion energy in the framework of both the critical radius $R_c$ and dynamic screening models. We show that it is possible to connect the $R_c$ and screening pictures through a single parameter, a charge defect $\sigma ,$ which depends on the charge state and the ratio between $R_c$ and the equilibrium bond length. Our data show that $R_c$ and hence $\sigma$ are slow varying functions of bond angle between $145°$ and $180°$ with $R_c\sim 4\mathrm{a}.\mathrm{u}.\mathrm{}$ and $\sigma \sim 0.5$ for the symmetric six-electron channel of ${\mathrm{CO}}_2.$ In the $R_c$ picture, the experimental value for $R_c$ is consistent with a theoretical value associated with ${\mathrm{CO}}_2^{3+},$ which is considerably smaller than that associated with ${\mathrm{CO}}_2^{+}(\sim 6\mathrm{a}.\mathrm{u}.\mathrm{}).\mathrm{}$

We suggest a simple method for measuring the temperature of ultracold gases made of fermions. We show that by using a two-photon Raman probe, it is possible to obtain line shapes which reveal properties of the degenerate sample, notably its temperature T. The proposed method could be used with identical fermions in different hyperfine states interacting via s-wave scattering or identical fermions in the same hyperfine state via p-wave scattering. We illustrate the applicability of the method in realistic conditions for ${}^6\mathrm{Li}$ prepared in two different hyperfine states. We find that temperatures down to ${0.05T}_F$ can be determined by this in situ method.

The dynamics of toroidal condensates in the presence of condensate flow and dipole perturbation have been investigated. The Bogoliubov spectrum of a condensate is calculated for an oblate torus using a discrete-variable representation and a spectral method to high accuracy. The transition from spheroidal to toroidal geometry of the trap displaces the energy levels into narrow bands. The lowest-order acoustic modes are quantized with the dispersion relation $\omega \sim |m|{\omega }_s$ with $m=0,\pm 1,\pm 2,\dots .$ A condensate with toroidal current $\kappa$ splits the $|m|$ co-rotating and counter-rotating pairs by the amount $\Delta E\approx 2|m|{ħ}^2\kappa 〈r^{-2}〉.$ Radial dipole excitations are the lowest-energy dissipation modes. For highly occupied condensates the nonlinearity creates an asymmetric mix of dipole circulation and nonlinear shifts in the spectrum of excitations so that the center of mass circulates around the axis of symmetry of the trap. We outline an experimental method to study these excitations.

We study the dynamical behavior of a Bose-Fermi mixture of trapped atomic gases which exhibits phase separation for a sufficiently strong repulsive interparticle interaction. For a dominantly bosonic mixture, the fermion density distribution and the associated single-particle spectra undergo a rapid change around the transition to the separated phase. Monopole strength distribution is studied in the random-phase approximation. The average energy calculated from the fermionic monopole strength shows a sharp minimum close to the transition point. The dynamical origin of the fermion single particle and collective properties is studied within a simple approximation.

We consider a continuous atom laser propagating through a waveguide with a constriction. Two different types of transmitted stationary flow are possible. The first one coincides, at low incident current, with the noninteracting flow. As the incident flux increases, the repulsive interactions decrease the corresponding transmission coefficient. The second type of flow only occurs for sufficiently large incident currents and has a solitonic structure. Remarkably, for any chemical potential there always exists a value of the incident flux at which the solitonic flow is perfectly transmitted.

We report experimental results on electromagnetically induced absorption spectra observed in the system which does not satisfy completely the conditions given by Lezama [Phys. Rev. A 59, 4732 (1999)]. We were able to observe electromagnetically induced absorption signals on all transitions in the Rb $D_1$ line, where $F_g\leftrightarrow F_e{=F}_g\pm 1$ or $F_g$ as well as open systems. These signals were only observed in certain Rabi frequency ranges for the coupling field. Present theoretical models, which are good for the case $F_g\leftrightarrow F_e{=F}_g+1,$ considering spontaneous transfer of atomic coherences or populations have not been able to explain our experimental results obtained in both cases $F_g\leftrightarrow F_e{=F}_g-1$ and $F_e{=F}_g.$

A pure state decoheres into a mixed state as it entangles with an environment. When an entangled two-mode system is embedded in a thermal environment, however, each mode may not be entangled with its environment by their simple linear interaction. We consider an exactly solvable model to study the dynamics of a total system, which is composed of an entangled two-mode system and a thermal environment. The Markovian interaction with the environment is concerned with an array of infinite number of beam splitters. It is shown that many-body entanglement of the system and the environment may play a crucial role in the process of disentangling the system.

We quantize the electromagnetic field in a polar medium starting with the fundamental equations of motion. In our model the medium is described by a Lorenz–type dielectric function $\epsilon (\mathbf{r},\omega )$ appropriate, e.g., for ionic crystals, metals, and inert dielectrics. There are no restrictions on the spatial behavior of the dielectric function, i.e., there can be many different polar media with arbitrary shapes. We assume no losses in our system so the dielectric function for the whole space is assumed as real. The quantization procedure is based on an expansion of the total field (transverse and longitudinal) in terms of the coupled (polariton) eigenmodes, and this approach incorporates all previous results derived for similar but restricted systems (e.g., without spatial or frequency dependence of coupled modes). Within the same model, we also quantize the Hamiltonian of a nonretarded electromagnetic field in polar media. Particular attention is paid to the derivation of the orthogonality and closure relations, which are used in a discussion of the fundamental (equal-time) commutation relations between the conjugate field operators.

We consider the relation between the orthogonality and the distinguishability of a set of arbitrary states (including multipartite states). It is shown that if a set of arbitrary states can be distinguished by local operations and classical communication (LOCC), each of the states can be written as a linear combination of product vectors such that all product vectors of one of the states are orthogonal to the other states. With this result we then prove a simple necessary condition for LOCC distinguishability of a class of orthogonal states. These conclusions may be useful in discussing the distinguishability of orthogonal quantum states further, understanding the essence of nonlocality and discussing the distillation of entanglement.

Plasmas offer the possibility of high acceleration gradients. An intriguing suggestion is to use the higher plasma densities possible in solids to get extremely high gradients. Although solid-state plasmas might produce high gradients they would pose daunting problems. Crystal channeling has been suggested as one mechanism to address these challenges. There is no experimental or theoretical guidance on channeling for intense electron beams. A high-density plasma in a crystal lattice could quench the channeling process. An experiment has been carried out at the Fermilab NICADD Photoinjector Laboratory to observe electron channeling radiation at high bunch charges. An electron beam with up to 8 nC per electron bunch was used to investigate the electron-crystal interaction. No evidence was found of quenching of channeling at charge densities two orders of magnitude larger than that in earlier experiments.